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Lec 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves. 
5.6 KB

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92.8 MB

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Lec 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves. 
77.7 MB


Lec 10: Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations. 
5.9 KB

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88.0 MB

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Lec 10: Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations. 
73.8 MB


Lec 11: Theory of General Secondorder Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians. 
5.9 KB

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95.9 MB

??B


Lec 11: Theory of General Secondorder Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians. 
80.4 MB


Lec 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constantcoefficient ODE's. 
4.7 KB

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88.0 MB

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Lec 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constantcoefficient ODE's. 
73.7 MB


Lec 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials. 
5.8 KB

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90.9 MB

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Lec 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials. 
76.2 MB


Lec 14: Interpretation of the Exceptional Case: Resonance. 
6.9 KB

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84.3 MB

184.9 MB


Lec 14: Interpretation of the Exceptional Case: Resonance. 
70.6 MB


Lec 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi). 
5.8 KB

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94.0 MB

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Lec 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi). 
78.8 MB


Lec 16: Continuation: More General Periods; Even and Odd Functions; Periodic Extension. 
5.7 KB

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93.8 MB

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Lec 16: Continuation: More General Periods; Even and Odd Functions; Periodic Extension. 
78.6 MB


Lec 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds. 
5.1 KB

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86.8 MB

188.9 MB


Lec 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds. 
72.7 MB


Lec 19: Introduction to the Laplace Transform; Basic Formulas. 
5.2 KB

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90.4 MB

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Lec 19: Introduction to the Laplace Transform; Basic Formulas. 
75.9 MB


Lec 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations. 
6.8 KB

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96.3 MB

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Lec 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations. 
80.7 MB


Lec 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's. 
5.7 KB

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96.9 MB

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Lec 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's. 
81.2 MB


Lec 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems. 
6.5 KB

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84.1 MB

??B


Lec 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems. 
70.5 MB


Lec 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs. 
5.6 KB

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83.7 MB

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Lec 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs. 
70.1 MB


Lec 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions. 
5.3 KB

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85.2 MB

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Lec 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions. 
71.4 MB


Lec 24: Introduction to Firstorder Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System. 
5.3 KB

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89.3 MB

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Lec 24: Introduction to Firstorder Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System. 
74.7 MB


Lec 25: Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case). 
5.9 KB

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93.1 MB

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Lec 25: Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case). 
78.1 MB


Lec 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues. 
6.2 KB

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88.4 MB

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Lec 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues. 
74.1 MB


Lec 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients. 
5.4 KB

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95.7 MB

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Lec 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients. 
80.1 MB


Lec 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters. 
5.5 KB

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89.0 MB

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Lec 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters. 
74.5 MB


Lec 29: Matrix Exponentials; Application to Solving Systems. 
6.1 KB

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92.7 MB

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Lec 29: Matrix Exponentials; Application to Solving Systems. 
77.8 MB


Lec 3: Solving Firstorder Linear ODE's; Steadystate and Transient Solutions. 
4.7 KB

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95.5 MB

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Lec 3: Solving Firstorder Linear ODE's; Steadystate and Transient Solutions. 
80.2 MB


Lec 30: Decoupling Linear Systems with Constant Coefficients. 
5.4 KB

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89.3 MB

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Lec 30: Decoupling Linear Systems with Constant Coefficients. 
74.8 MB


Lec 31: Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Nonlinear Pendulum. 
6.0 KB

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89.5 MB

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Lec 31: Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Nonlinear Pendulum. 
75.2 MB


Lec 32: Limit Cycles: Existence and Nonexistence Criteria. 
5.2 KB

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87.0 MB

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Lec 32: Limit Cycles: Existence and Nonexistence Criteria. 
72.9 MB


Lec 33: Relation Between Nonlinear Systems and Firstorder ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle. 
4.7 KB

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95.1 MB

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Lec 33: Relation Between Nonlinear Systems and Firstorder ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle. 
79.8 MB


Lec 4: Firstorder Substitution Methods: Bernouilli and Homogeneous ODE's. 
6.2 KB

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95.2 MB

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Lec 4: Firstorder Substitution Methods: Bernouilli and Homogeneous ODE's. 
79.8 MB


Lec 5: Firstorder Autonomous ODE's: Qualitative Methods, Applications. 
6.3 KB

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86.8 MB

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Lec 5: Firstorder Autonomous ODE's: Qualitative Methods, Applications. 
72.8 MB


Lec 6: Complex Numbers and Complex Exponentials. 
5.5 KB

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86.2 MB

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Lec 6: Complex Numbers and Complex Exponentials. 
72.2 MB


Lec 7: Firstorder Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods. 
7.0 KB

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78.1 MB

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Lec 7: Firstorder Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods. 
65.4 MB


Lec 8: Continuation; Applications to Temperature, Mixing, RCcircuit, Decay, and Growth Models. 
5.5 KB

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96.0 MB

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Lec 8: Continuation; Applications to Temperature, Mixing, RCcircuit, Decay, and Growth Models. 
80.3 MB


Lec 9: Solving Secondorder Linear ODE's with Constant Coefficients: The Three Cases. 
5.5 KB

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94.8 MB

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Lec 9: Solving Secondorder Linear ODE's with Constant Coefficients: The Three Cases. 
79.5 MB

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MIT18.03S06_files.xml  Metadata  [file] 
MIT18.03S06_meta.xml  Metadata  2.1 KB 
MIT18.03S06_reviews.xml  Metadata  657.0 B 
Other Files  Archive BitTorrent 

MIT18.03S06_archive.torrent 
91.4 KB
